Page 342 - Tunable Lasers Handbook

m A
0.8 ‘‘OI
302 Norman P. Barnes

gain

.- -

0.4
z Threshold

0.2

I I
0 0.5 1 .o 1.5
Normalized Time (Ut,)
FIGURE 2 Pulsed gain as a function of time showing instantaneous threshold.

exponential gain. Because of this large gain. the difference between an observ-
able threshold that produces 1 .O or 10.0 pJ is relatively small.
In the cw parametric oscillator, a mode gain can be determined under
threshold conditions. Because the pump beam will not be significantly depleted
at threshold. the longitudinal variation of the pump beam may be neglected.
Because the product of two Gaussian beams is another Gaussian beam, interact-
ing beams will generate a nonlinear polarization, which is also a Gaussian. If the
electric fields at wavelengths h2 and h, interact, they will generate a nonlinear
polarization at wavelength h,, which will have a spatial variation characterized
by a beam radius given by

Note that the generated nonlinear polarization does not necessarily have the
same spatial variation as the incident field at A,. Because of the potential mis-
match between the incident electric field and the generated electric field. the gain
coefficient will have an additional term to account for this effect [6]. Including
this term in the gain expression yields